6544
stitution in the perpendicular allyl cation XXIII provides a slight stabilization (-1.9 kcal mol-’, eq 12), but 1-methyl substitution produces a much larger effect in going from I11 to XXIV (-20.4 kcal mol-’, eq 13). Stereomutation of XXII should proceed through the 1methylcyclopropyl cation (XXIV) since methyl substitution favors path B over path A by 18.5 kcal mol-’. Electron releasing substituents, R ”, which stabilize carbonium ions to a greater extent than methyl should favor path B even more. In the extreme such substituents might even render the 1-substituted cyclopropyl cations more stable than their 2-substituted allyl counterparts. From known thermochemical dataAg and theoretical stabilization energies of substituted methyl cations,60it would appear that methoxy, hydroxy, and amino groups should be such substituents. Abundant experimental evidence is available already. Many cyclopropane substitutions are known involving 1-ROand l-R2N-cyclopropyl cation intermediates ; these proceed without ring opening.61 The stable l-dimethyl(59) R. H. Martin, F. W. Lampe, and R. W. Taft, J . Amer. Chem. SOC.,88,1353 (1966). (60) J. A. Pople, submitted for publication. (61) W. J. M. van Tilborg, S. E. Schaafsma, H . Steinberg, and Th. J. deBoer, R e d . Trau. Chim. Pays-Bas, 86, 417 (1967); J. Szmuskovica, D . J. Duchamp, E. Cerda, and C. G. Chidester, Tetrahedron Lett., 1309 (1969); H . H . Wasserman and M. S. Baird, ibid., 1729 (1970), 3721 (1971); W. J. M. van Tilborg, G. Dooyewaard, H . Steinberg, and Th. J. deBoer, ibid., 1677 (1972); a case which may involve a l-fluorocyclopropyl cation is also known: P. Weyerstahl, G . Blume, and C. Miller, ibid., 3869 (1971).
aminocyclopropyl cation has been observed directly. In addition, reactions involving cyclopropyl cations stabilized by l - a r ~ l l, -~c ~y c l o p r ~ p y l ,l-alken~l,~b ~~ and 1-thiophenoxy5bb groups are known which proceed with only partial ring opening. However, despite attempts,66 no cases of closure of 2-substituted allyl cations to 1-stabilized cyclopropyl cations have been discovered yet6’ The problems appear to be practical rather than thermodynamic. Acknowledgment. We thank Professor J. Hauser (Duquesne University) for helpful discussions. This work was supported in Princeton by National Science Foundation Grant G P 29078X, the Petroleum Research Fund, administered by the American Chemical Society, and Hoffmann-LaRoche, Inc., Nutley, N. J. Work at Carnegie-Mellon was supported by the National Science Foundation under Grant GP25617. (62) E. Jongejan, W. J. M. van Tilborg, Ch. H. V. Dussen, H. Steinberg, and Th. J. deBoer, TefrahedronLetf.,2359 (1972). (63) D. B. Ledlie and E. A. Nelson, Tefrahedron Lett., 1175 (1969); D. T. Clark and F. Smale, Chem. Commun., 868 (1969); W. J. M. van Tilborg, J. R. van der Vecht, H. Steinberg, and Th. J. deBoer, TefrahedronLeft., 1681 (1972). (64) J. A. Landgrebe and L. W. Becker, J. Amer. Chem. Soc., 89, 2502 (1967); 90, 395 (1968); B. A. Howell and J. G. Jewett, ibid., 93, 798 (1971). (65) M. L. Poutsma and P. A. Ibaria, Tefrahedron Lett., 4967 (1970). (66) H. M. R. Hoffmann, private communication, Sept 1971. (67) For an apparent exception, see D. Cantacuzbne and M. Tordeux, Tetrahedron Lerr., 4807 (1971); J. C. Blazjewski, D. Cantacuzene, and C. Wakselman, Tetrahedron, in press.
Molecular Orbital (CNDOI2 and MINDO) Calculations on Protonated Deoxyribonucleic Acid Bases. The Effects of Base Protonation on Intermolecular Interactions Frank Jordan” and H. Dirk Sostman Contribution f r o m the Department of Chemistry, Rutgers University, Newark, New Jersey 07102. Received December 19, 1972
Abstract: The electronic reorganization accompanying monoprotonation of DNA bases was examined employing all-valence-electronSCF molecular orbital methods. u as well as T reorganization upon protonation is evident
in all four bases. Stacking and hydrogen-bonding interactions were calculated including monopole-monopole, monopole-induced dipole, and dispersion terms between the various bases in their neutral and monoprotonated states for all possible combinations. The intermolecular interactions are invariably moie favorable for half-protonated pairs (i.e., one base protonated) than for neutral pairs. Stacking interactions are always unfavorable in doubly protonated pairs (Le., both bases protonated). part of a continuous program in this laboratory to A examine the effect of the state of ionization of nucleic acid components on their electronic structures s
and intermolecular interactions, recently all-valenceelectron C N D 0 / 2 and MINDO SCF calculations were reported on some adenine tautomers and their protonated analogs. This contribution completes our studies at the level of approximation of base interaction only. Electronic structures of all four protonated bases, adenine (A), (1) F. Jordan and H . D . Sostman, J. Amer. Chem. SOC.,94, 7898 (1972).
JournaI of the American Chemical Society 1 95:20
guanine (G), thymine (T), and cytosine (C), are described and an attempt is made to predict their interbase interactions both in the vertical (stacking) and horizontal (in-plane) hydrogen-bonding mode. The theoretical approaches employed are the same as those previously reported, the CND0/23” and (2) Some other abbreviations used are poly T, poly A, poly G, poly C, and poly U for the homopolymers and ApA, ApG, ApC, etc., for the dinucleoside monophosphates, For example, ApA would have a 0 - 3 ’ and a 0 - 5 ’ bound adenosine attached to the phosphate. (3) (a) J. A , Pople and G. A. Segal, J . Chem. Phys., 44, 3289 J1966); Quantum Chemistry Program Exchange No. 91; (b) N. C. Baird and M. J. S. Dewar, ibid., 50, 1262 (1969); Quantum Chemistry Program Exchange No. 137.
October 3, 1973
6545 Table I. Energy, Dipole Moments, and Ionization Potential of Neutral and Protonated DNA Bases Molecule or ion
Total energy* or AHf, kcal/mol
TotalCdipole moment, D
ud dipole moment, D
C M C M C M C C M C
-60,964.1 -101.13 -61,171.1 -14.87 -12,651.2 -83.11 -78,064.8 -72,764.9
2.99 2.30
1.25 1.78 3.58 2.66 3.93
C M C C M C
-55,374.4 -221.00 - 58,872.6 - 53,920.3 t10.98 - 59,399 .Q
7.71 8.14 7.39
C M C C M C
- 62,739.07
4.23
Methoda
IP,e eV
Geometry employed'
~~
Adenine Adenine Adenine N-1 H+ Adenine N-1 H+ Guanine Guanine N-9 CHs Guanine N-7 H+ Guanine N-9 CH: N-7 Hf Cytosine Cytosine N-1 CHa Cytosine N-3 Hf Cytosine N-1 CHs, N-3 H+ Thymine Thymine N-1 C H j Thymine 0 - 4 H+ Thymine 0 - 4 H+, N-1 CHa
7.25 7.09 7.00
4.70
-78,225.3
-220.57 -68,137.92 - 63,078.3 -87.27 -68,364.21
2.65 3.74
2.00
4.18 5.15
10.3 9.0 16.2 13.9 9.74 9.22 9.57 15.78 14.33 15.69
P, H;@I, Ch P, H;' I, Ch P, C;A I, Ch P, C;A I, C* P, 0;' I: oi
10.83 10.1 10.6 18.1 15.4 17.0
BM' BM' BM BT" BTm BT"
11.79 10.51 11.45 17.68 15.34 16.99
Ha
+
P, 0;i I, 0 Md P, ST;k I, STk P, ST;k I, STk
+ Mi
Ha ST" ST" ST"
+ Mi
* According to CND0/2 including nuclear repulsions, according to MINDO heat of formation. a C = CNDO/2; M = MINDO. Including net charges and hybrid moments as in ref 3a. Based on u charges only assuming two u electrons 011 an imidazole N-H type nitrogen and one s electron on a pyridine like nitrogen. e Given by the negative of the energy of the highest occupied molecular orbital according to Koopmans' theorem. f P = pyrimidine geometry; I = imidazole geometry. 0 H. K. Hoogsteen, Acta Crystallogr., 16, 907 (1963). C. W . Cochran, ibid., 4, 81 (1951). 0: 0. J. O'Brien, ibid., 23, 92 (1967). i Methyl constructed according to Hoogsteen's parameters in g. k ST: H. M. Sobell and K. I. Tomita, Acta Crysrallogr., 17, 126 (1964). BM: D. L. Barker and R. E. Marsh, ibid., 17, 1581 (1964). m BT: C. F.BryanandK. LTomita, ibid., 15,1174 (1962). li ST: H. M. SobellandK. LTomita, ibid., 17, 122 (1964). MIND03bmethods with their original parametrizations. The very simple approximation employed in calculating the intermolecular interactions was described earlier. Briefly, it uses CNDOj2 or MINDO charge densities, isotropic bond polarizabilities, and MINDO ionization potentials (the much more reasonable value of the two) to calculate the interaction energy as a sum of monopole-monopole, monopole-induced dipole, and dispersion terms. Since the calculations are performed for ionic species, the dipole-dipole approximation cannot be used, the dipole moment of a charged species being origin dependent. Partially due t o economy (since a large number of calculations had to be performed), we only report on results using CND0/2 charge densities. This we can justify since our previous report indicated no major differences in interaction energies based on CND0/2 or MINDO charges and because others have shown that CNDOj2 is more reliable in its dipole moment predictions than is MINDO. The report is logically broken down into two parts; the effect of protonation on the DNA base electronic structure, and the effect of protonation on interbase interactions. Several experimental contributions called our attention to this topic and certainly the well known pK, of the conjugate acids5 of the DNA bases assures that a significant, if small, number of cytosine and adenine components would be protonated under physiological conditions.
The Electronic Effects of Base Protonation One can note the effects of base protonation on a number of molecular orbital parameters. Among these are the electronic reorganization (in the u and T distributions and in the T moment which unlike the total molecular moment remains origin independent on protonation) and ionization potential changes. Table I presents all the gross features of the C N D 0 / 2 and MINDO calculations employing X-ray crystallographic geometries. The total energies are not considered to be of great significance in this study but are quoted for comparison with other studies on these molecules. The ionization potentials (given by the negative of the highest occupied molecular orbital energy level according to Koopmans' theorem) are consistently increased upon protonation of the base by as much as 50% or more in the four cases studied. Such increases in ionization potentials were also found by the ab initio calculations on HzO and H30+.' The ionization potentials enter the intermolecular energy calculations, their relative magnitudes being of great importance in the dispersion calculations. Charge Reorganization upon Protonation. CNDOj2 and MINDO calculations were performed for each system for several reasons. MINDO provides more realistic ionization potentials than CNDOj2 but usually less realistic electron density pictures. The questions of interest in comparing the neutral and protonated bases are: how do the u and T frame-
(4) G. Klopman, "Topics in Current Chemistry," Vol. 15, No. 4, Springer-Verlag, West Berlin, 1970. ( 5 ) R. M. Izatt, J. J. Christensen, and J. H. Rytting, Chem. Rea., 71, 439 (1971).
(6) D. B. Boyd, J . Amer. Chem. SOC.,94,64 (1972). (7) P. A. Kollman and L. C. Allen, J. Amer. Chem. SOC.,92, 6104 (1970).
Jordan, Sostman
C N D O / 2 and M I N D O Calculations on Protonated DNA Bases
6546 Table III. -T and Net Atomic Charges in Adenine (A) and N-1 H + Adenine (AH+), MINDO"
,'I--c-"-" i-. CM
-r
Atom N-1 c-2 N-3 C-4
c-5
C-6 N-7 C-8 N-9 N-6 N-1 H C-2 H C-8 H N-9 H N-6 Hb
0la.in.
Q
m
Y
A -0.563 +O ,405 -0.509 $0. 246 -0.255 4-0.397 -0.515 1-0.322 +0.316 $0.156
Total atomic charges-chargesAH+ Traiisfer A AH+ Transfer -0.727 $0 ,413 -0.470 $0.272 -0.249 +0.387 -0.529 $0.358 +0.334 $0.211
-0.164 $0.008 +0.038 +O, 025 +0.006 -0.009 -0.013 +0.035 $0.017 $0.055
-0.703 $0.690 -0.638 +O ,570 -0.101 +0.708 -0.490 $0.597 -0.605 -0.708 -0.031 -0.045 $0.221 $0.268
-0.742 $0.710 -0.501 +O. 577 -0.078 $0.741 -0.421 +O ,641 -0.590 -0.703 $0.319 1-0.032 +0.029 +0.313 +0.337
-0.039 $0.020 10.137 +O ,006 $0.023 $0.032 +0.069 $0 ,044 $0.014 10.004 -0.680 1-0.063 $0.074 $0.091 +0.069
The average of two amino
Figure 1. Numbering system and unrotated geometries of bases.
See footnotes a-c in Table 11. hydrogen values.
works react to protonation, and how does the attacking proton adjust to its new environment. While many calculations have been published on the neutral bases,6 no comparison with protonated ones is available ; therefore, such a comparison is presented below. Figure 1 describes the numbering system employed. Adenine. The a-electron density on the nitrogen being protonated decreases substantially while its total electron density decreases (CND0/2) or changes very little (MINDO) (Tables I1 and 111). Protona-
some findings on nucleotides8 and nucleotide zwitterionsg (N- 1 protonated, monophosphate monodeprotonated) obtained by extended Hiickel calculations. The latter confined the effects of protonation to the pyrimidise ring; however, these calculations did not allow for charge iteration so that these results are not surprising. As Table I indicates the 7r moment increases upon protonation independent of the method employed. Guanine. The a-electron density is increased substantially at N-7 (site of protonation), N-1, and N-3 upon protonation according to both methods (Tables IV and V). The total electron density is increased at
Table 11. T and Net Atomic Charges in Adenine (A) and N-1 H + Adenine (AH+), C N D O / P ~~~
---T
Atom
A
~~~
Total atomic charges*A h a r g e s AH+ Transfer A AH+ Transferc ~ _ _ _ _ _ _ ~
N-1 C-2 N-3 C-4 C-5 C-6 N-7 C-8 N-9 N-6 N-1 H C-2 H C-8 H N-9 H N-6 Hd
-0.276 $0.109 -0,205 $0.044 -0,158 f0.154 -0,232
-0,611 +0.094 -0,137 +0.061 -0,136 $0,221 -0,528 fO.O1O +0.359 +0.397 +0.430 $0.155 $0.247
-0.335 -0.014 $0.067 $0.016 +0.022 +0.066 -0.296 +0.348 $0.033 +0.091
-0.296 1-0.209 -0.226 $0.218 -0.067 $0.256 -0.261 $0.167 1-0.084 -0.248 -0,030 t0.009 3-0.109 $0.122
-0.138 +0.236 -0.153 t0.221 -0.017 +0.344 -0,139 $0.174 -0.119 -0.207 $0.171 +0.047 $0.046 $0.178 +0.178
$0.158 $0.027 $0.072 t0.003 +0.049 $0.087 $0.122 $0.007 -0.034 $0.041 -0.828 +0.078 +0.036 1-0.068 $0.055
Geometries used are the same as those in Table I. * T charges derived from the orbital electron population of the atomic orbital perpendicular to the molecular planes. Transfer of electron density on protonation; a negative value indicates that the atom has become electron richer on protonation; a positive value shows The average of two amino electron density loss on protonation. hydrogen values.
tion decreases the total electron density at all atoms to varying degrees, except for the slight increase predicted at N-9 according to CNDO/2. On the whole, all atoms undergo changes in charge upon protonation, the changes being more pronounced according to C N D 0 / 2 than according to MINDO. These substantial changes in SCF base charges are at variance with Journnl of the American Chemical Society
Table IV. T and Net Atomic Charges in Guanine (G) and N-7 H + Guanine (GH +). CNDO/2& ---r
Atom N-1 C-2 N-3 C-4 C-5 C-6 N-7 C-8 N-9 N-2 0-6 N-1 H N-7 H C-8 H N-9 H N-2 Hb
G $0.287 f0.200 -0,392 $0.083 -0,240 $0.188 -0,134 -0.045 +0.345 +0.171 -0.464
chargesGH' Transfer +0.262 f0.242 -0.432 +0.101 -0,253 +0.156 -0,457 $0.125 +0.410 1-0.207 -0.362
-0.025 +0.042 -0,040 +0.017 -0,013 -0,032 -0,323 +0.170 +0.065 +0.035 +0.101
See footnotes a-c in Table 11. hydrogen values.
--
Total atomic chargesG GH+ Transfer
-0.221 +0.382 -0,328 +0.218 -0,111 +0.355 -0,160 +0.140 -0.142 -0.251 -0.385 +0.119
-0.249 $0.422 -0.310 +0.266 -0.092 +0.381 -0.001 $0.241 -0.117 -0.241 -0.300 $0.182 $0.193 -0,009 1-0.078 f0.116 $0.195 +0.139 +0.175
* The
-0.028 3-0.040 $0.018 3-0.048 +O.O18 f0.026 +0.159 3-0.1O1 4-0.024 f0.009 3-0.085 $0.063 -0.806 +0.087 $0.079 3-0.036
average of two amino
N-1 and at the incoming proton again upon protonation. All other atoms distribute the resulting loss in electron density. The 7r moment increases upon protonation but shows a much smaller fractional increase than does the 7r moment of adenine (Table I). (8) D. B. Boyd and W. N. Lipscomb, J. Theor. Biol., 25,403 (1969). (9) F. Jordan, unpublished results.
1 95:20 1 October 3, 1973
6547 Table V. n and Net Atomic Charges in Guanine (G) and N-7 H + Guanine (GH +), MINDO" a -
Atom N-1 C-2 N-3 C-4 C-5 C-6 N-7 C-8 N-9 N-2 0-6 N-1 H N-7 H C-8 H N-9 H N-2 Hb
G +0.230 +0.462 -0,647 +0.262 -0.329 $0.451 -0,447 +0.289 +0.271 +0.148 -0.693
Total atomic charges------chargesGH+ Transfer G GH+ Transfer +0.204 +0.482 -0,676 +0.241 -0.329 $0.425 -0.598 +0.382 +0.290 $0.184 -0.606
-0.026 +0.019 -0.029 -0.020 -0.000 -0.026 -0.151 +0.092 +0.019 $0.036 +0.086
a See footnotes a-c in Table 11. hydrogen values.
-0.783 $0.919 -0.658 +0.577 -0.148 +0.882 -0.399 +0.605 -0.640 -0.696 -0,653 +O. 307
-0.838 +0.928 -0.576 $0.591 -0.128 $0.922 -0.456 $0.660 -0.630 -0.687 -0.574 $0.373 $0,332 -0.061 $0.034 $0.247 $0.364 +0.251 $0.341 b
-0.054 t0.009 +0.082 +0.013 $0.020 +0.039 -0.057 $0.055 +0.010 $0.008
+0.079 +O ,065
-0.667 $0.096 +0.116 $0.090
Atom
C
Total atomic A h a r g e s C CH+ Transfer
chargesCH+ Transfer +0.346 +0.166 -0.645 +0.287 -0.217 $0.235 +0.240 -0.413
-0.188 $0 ,422 -0,345 +O. 326 -0.184 +0.188 +O ,244 -0,414 +0.134
+0.025 -0.034 -0.279 +0.070 -0.016 +0.098 $0.037 +0.098
a See footnotes a-c in Table 11. hydrogen values.
Atom
C
N-1 C-2 N-3 C-4 C-5 C-6 N-4 0-8 N-1 H N-3 H C-5 H C-6 H N-4 H*
+0.236 +0.498 -0.579 $0.425 -0.299 $0.271 +0.180 -0.734
charges-charges-CH+ Transfer C +0.250 +0.469 -0.731 +0.437 +0.372 -0.325 +0.207 -0.680
+0.013 -0.029 -0.151 +0.012 +0.671 -0.597 +0.026 +0.054
CH+ Transfer
-0.752 +1.068 -0.720 +0.756 -0.314 +0.505
-0.713 -0.667 +O. 295 $0.055
-0.083 +0.285
-0.705 +0.046 $1.079 $0.011 -0.731 -0,011 +0.785 1-0.029 -0.270 $0.043 $0.533 +0.028 -0.655 +0.058 -0.562 +0.104 + O . 387 +O. 092 $0,353 -0.646 +0.134 +0.079 $0.011 +0.094 $0.319 +0.034
~~
See footnotes a-c in Table 11. hydrogen values. a
b
The average of two amino
Table VIII. a and Net Atomic Charges in Thymine (I) and 0 - 4 H + Thymine (TH+), CNDOLP
Table VI. n and Net Atomic Charges in Cytosine (C) and N-3 H + Cytosine (CH+), CNDO/ZU
N-1 +0.321 C-2 1-0.200 N-3 -0.366 C-4 +0.217 C-5 -0.201 C-6 $0.136 N-4 +0.203 0-8 -0.512 N-1 H N-3 H C-5 H C-6 H N-4 Hb
Total atomic -n
The average of two amino
Cytosine. The only point of general agreement between C N D 0 / 2 and M I N D 0 in this case concerns the decreased x charge on the nitrogen (N-3) being protonated. Almost all net atomic charges (except attacking proton) become more positive upon protonation, N-3 and 0 - 8 bearing most of the change (Tables VI and VII), A rather large increase in x moment ac-
-n
Table VII. ?r and Net Atomic Charges in Cytosine (C) and N-3 H Cytosine (CH+), MINDO"
-0.135 $0.053 +O. 472 $0.050
-0.143 $0.414 -0.144 +0.276 -0.187 -0.272 +0.205 $0.192 -0.001 -0.089 $ 0 . 043 $0.045 $0.131 +0.182
b
$0.202 +0.088 +0.039 +0.088 +0.057 $0. 141 $0.070 -0.807 -0.087 $0.001 $0.051
The average of two amino
companies protonation. Of the four neutral bases cytosine appears to have the smallest fractional Rmoment contribution to the total moment. Thymine. Tables VI11 and IX provide the charge densities on neutral and 0 - 4 protonated thymine. Interestingly, the r-electron density substantially increases on the oxygen to which the proton is being attached, while its net atomic charge changes much less in the opposite direction. CND0/2 indicates electron density increases at some carbon atoms upon protonation. Again a substantial x-moment increase is noted upon protonation. As we showed in our previous work,' the dipole moments and ionization potentials appear to be less sensitive to geometric changes than are the total energies
---T
T
Atom N-1 c-2 N-3 C-4 C-5 C-6 0-2 0-4 c-5' N-1 H N-3 H C-6 H C-5' Hb 0-4 H
charges-chargesTH+ Transfer T
$0.249 +0.393 +0.144 +o, 196 +o, 164 -o,032 +0.260 +0.187 -0.108 +0.062 -0.451 -0.396
+0.322 f0.269 -0.162 +0.233 -0.403 -0.818
+0.062 +0.081 -0.053 +0.171 +0.047 -0.421
See footnotes a-c in Table 11. methyl hydrogens.
Total atomic
-0.207 +o,447 -0.259 +0.346 -0.095 +0.137 -0.360 -0.343 -0.016 +O. 150 i0.006 +O. 141 +0.017
TH+ Transfer -0.130 +o,445 -0,212 +0.429 -0.102 $0,247 -0.287 -0.188 -0.014 t o .197 i o . 191 +0.064 +0.042 +0.231
+0.076 -o,oo2 $0.046
+0.083 -0.006 $0.109 +0.073 +0.154 $0.002 +0.046 +O. 185 -0.076 +0.025 -0.768
* The average value for the three
Table IX. a and Net Atomic Charges in Thymine (T) and 0 - 4 H + Thymine(TH+), MINDOa -n
Atom
T
Total atomic charges-Bharges-TH+ Transfer T TH+ Transfer
~~~~
+D 195 +O 284
-0 731 -0 695 $1 115 +1 090 -0 810 -0 795 +O 892 +O 897 C-5 -0 246 -0 312 -0 065 -0 325 -0 353 +O 234 $0 376 +O 142 +O 473 +O 579 C-6 0-2 -0.704 -0.681 +0.022 -0.670 -0.543 0-4 -0.675 -0.866 -0 190 -0.670 -0.665 +0.363 +0.360 c-5' N-1 H f0.332 +0.359 N-3 H -0.067 $0.346 C-6 H $0.293 +0.016 C-5' Hb -0.064 -0.017 $0.455 0-4 H N-1 C-2 N-3 C-4
+O 088 +O 492 +O 482 -0 009 +O 227 +O 250 +O 023 +O 477 +O 465 -0 011
a See footnotes a-c in Table 11. methyl hydrogens.
036 025 015 005 028 +O 106 +0.127 +0.005 -0.003 +0.027 +0.413 -0.277 +0.046 -0,544 $0 -0 $0 +O -0
* The average value for the three
of the systems. While not much experimental data are available on the dipole moments of the bases, the two methods MINDO and C N D 0 / 2 usually are in qualitative agreement with each other, the latter giving closer agreement with experiment. Perhaps what is remark-
Jordan, Sostman / CNDOI2 and MINDO Calculations on Protonated DNA Bases
6548
able is the relative agreement between the moments given by MINDO and CND0/2 in spite of the grossly different charge densities predicted by the two methods. We have also shown’o that with a reasonable parametrization even the uniterated extended Huckel theory can provide dipole moments in good agreement with those provided by the present SCF methods. Notwithstanding the correct dipole moment predictions, one would expect SCF charges to be more correct. Although protonation takes place in the plane of the system, a substantial perturbation of the K system is evident. K reorganization is more extensive in adenine than in guanine, the imidazole ring of both being strongly affected even though only guanine is protonated on this ring (N-7). K reorganization is somewhat more extensive in thymine than in cytosine; e.g., in thymine the N-1 atom is more susceptible to 0 - 4 protonation than is the N-1 atom in cytosine to N-3 protonation. The u system appears to be less active in charge delocalization than is the K system. The charge of the heteroatom being protonated absorbs a large fraction of the plus charge introduced by the incoming proton. Another interesting observation is that the change in net atomic charge upon protonation does not follow the accepted electronegativity relationships of the particular atoms. Doty, et aZ.,ll showed that some changes occur in the uv spectra of the bases upon protonation. Presumably, such changes would be related to K reorganization. 13Cnmr studies should prove helpful in checking the validity of our findings.
Intermolecular Interactions Theoretical Considerations. To our knowledge this work represents the initial attempt to account for the effects of protonation on DNA interactions. Because of the size of the molecules and the approximations involved in gathering the various input parameters needed for an intermolecular interaction calculation (such as net atomic charges, ionization potentials, bond polarizabilities), it was felt that a relatively approximate solution is in order. Many groups have calculated the base-base interactions between neutral species l 2 starting with the classic work of De Voe and Tinoco. l Z a We are here attempting t o incorporate the effects of protonation on such interactions. A considerable amount of theoretical work has been performed on intermolecular interactions and the progress is summarized by Hirschfelder, Curtiss, and Bird13 and Margenau and Kestner. l 4 As in our previous contribution, we again adopt an approximation for intermolecular forces easily applicable to such large systems for a variety of geometrical variations. (10) F. Jordan, Biopolymers, 12,243 (1973). (11) D. Voet, W. B. Gratzer, R . A. Cox, and P. Doty, Biopolymers, 1, 193 (1963). (12) (a) H . D e Voe and I. Tinoco, Jr., J . Mol. Biol., 4, 500 (1962); (b) H. A. Nash and D. F. Bradley, Biopolymers, 3, 261 (1965); (c) A. Pullman and B. Pullman, Adoan. Quantum Chem., 4 , 267 (1968); (d) B. Pullman, “Molecular Associations in Biology,” B. Pullman, Ed., Academic Press, New York, N. Y.,1968; (e) R . Rein, P. Claverie, and M. Pollak, In?. J . Quantum. Chem., 2, 129 (1968). (13) J. 0. Hirschfelder, C. F. Curtiss, and R . B. Bird, “Molecular Theory of Gases and Liquids,” Wiley, New York, N. Y., 1964, Chapters 12 and 13. (14) H . Margenau and N. R. Kestner, “Theory of Intermolecular Forces,’’ Pergamon Press, Oxford, 1969.
We assume point charges at the atoms as given in Tables 11, IV, VI, and VI11 (CND0/2) to calculate the monopole-monopole interaction energy ( p p ) between groups of such charges. The monopole-induced dipole (polarization) energy ( p a ) is calculated using isotropic bond polarizabilities. l5 Finally, the dispersion energy (aa)is calculated with the use of molecular (or ionic) ionization potentials and isotropic bond polarizabilities. The appropriate equations are given in ref 1 and are a further simplified variation of a recent calculation by Rein, et al. l 6 We have employed MINDO ionization potentials since these appear to be closer (see Table I) to the experimentally reported values where such are available (calculated in electron volts by MINDO for A, 9.0; C, 10.1; T, 10.5; experimental’’ for A, 8.90; C, 8.90; T, 9.43). Rein, et al.,’* in their most recent contribution showed that in the interaction of two pyridine molecules quadrupole terms may be dominant at interaction distances of less than 10 A. N o such calculations for DNA bases are available. According t o electrostatic theory both dipole and quadrupole moments of ions vary with the origin assumed, and the dipole moment is zero at the center of charge. In order to retain the simplest consistent approximation we only calculate monopole-monopole, monopoleinduced dipole, and dispersion terms as before. These terms can be calculated with ease for any interacting system irrespective of the charge of the species. More rigorous theoretical attempts have tried to decompose hydrogen-bonding interactions into electrostatic, exchange, charge-transfer, polarization, and dispersion terms.19 Each term was shown to lead to significant contributions to the total energy. While we are accounting for most of these terms, the possibility of charge transfer at hydrogen-bonding or stacking distances is not taken into account in the present work. In order to see if there is significant charge transfer according to CNDO/2, one needs to compute eigenvalues and eigenfunctions of the entire system. This we will attempt in the future. Stacking Interactions. In order to be able to compare the stacking interactions between adjacent bases as a function of the state of protonation, all calculations were performed at 3.30-w interplanar separation. This value represents an average of the interplanar separations in similar molecules compiled by Bugg, et Calculations were performed for a large variety of rotational and translational variations at the 3.30-A interplanar separation. The zero rotation places all molecules in the X-Y plane and centers the C-4-C-5 bond of purines and the N-1-C-4 bond of pyrimidines along the Y axis as indicated in Figure 1. Molecule (or ion) 1 was held stationary and molecule (or ion) 2 was rotated clockwise in ( 1 5 ) R. J. W. Le Fivre, Adcan. Phys. Org. Chem., 3, l(1965). (16) M. S . Rendell, J. P. Harlos, and R. Rein, Biopolymers, 10, 2083
(1971). (17) C. Lifschitz, E. D. Bergmann, and B. Pullman, Tetrahedron Lett., 4583 (1967); employing mass spectrometry. (18) R. Rein, J. R. Rabinowitz, and T. J. Swissler, J . Theor. Biol., 34, 215 (1972). (19) P. A. Kollman and L. C. Allen, Chem. Reo., 72,283 (1972). (20) (a) C. E. Bugg, J. M. Thomas, M. Sundaralingam, and S . T. Rao, Biopolymers, 10, 175 (1971); (b) C. E. Bugg, “The Purines Theory and Experiment, Jerusalem Symposia on Quantum Chemistry and Biochemistry IV,” The Israel Academy of Sciences and Humanities, Jerusalem, 1972.
Journal of the American Chemical Society 1 95:20 1 October 3, 1973
6549 Table X. Optimal Stacking Interaction Energies and Corresponding Geometries"
Stationary
Rotated, translated species
Geometrical* definition of variable species RA, o TRA, o RTD, A
---Interaction PPC
-
energies, kcal/mol
pa (1)d
Pff (2Y
fffff
-0.09 -0.10 -0.08 -1.20 -0.34 -0.34 -1.31 -0.57 -0.45 -1.04 -0.33 -0.40 -1.15
-0.08 -0.11 -4.92 -4.75 -1.20 -0.37 -3.90 -1.31 -0.57 -4.85 -1.04 -0.34 -5.32 -1.15
-7.85 -8.03 -9.97 -9.79 -2.17 -7.51 -9.26 -1.90 -7.33 -6.70 -1.45 -6.31 -7.12 -1.38
-8.43 -8.54 -16.96 -16.56 39.50 -9.69 -18.85 38.77 -12.96 -17.17 39.93 -8.95 -16.75 43.02
-0.23 -0.36 -4.88 -1.17 -0,72 -0.50 -6.72 -1.26 -0.37 -0.50 -6.67 -1.44 -0.37 -0.47 -5.81 -1.49 -0.62 -0.55 -5.99 -1.33 -0.35 -0.45 '-4.81 -1.02
-0.09 -3.99 -0.10 -1.28 -0.08 -3.14 -0.08 -1.03 -0.07 -3.14 -0.06 -1.01 -0.27 -3.28 -0.33 -0.97 -0.24 -3.98 -0.28 -0.99 -0.54 -4.63 -0.45 -1.18
-7.58 -9.03 -10.10 -1.96 -7.42 -7.54 -9.24 -1.78 -6.95 -7.75 -8.89 -1.74 -6.71 -8.20 -7.67 -1.57 -7.35 -7.98 -8.09 -1.60 -6.84 -6.36 -7.02 -1.42
-9.51 -17.97 -17.54 39.68 -9.84 -15.7C -18.35 40.38 -8.99 -16.32 -18.54 41.67 -10.26 -16.22 -19.27 41.15 -12.08 -17.16 -18.83 39.63 -11.77 -16.64 -16.81 41.46
&tal'
Homogeneous Pairs A
A
AH+
A
AH+ G GH+ GH+ T TH+ TH+ C CH+ CH+
AH+ G G GH+ T T TH+ C C CH+
A AH+ A AH+ A AH+ A AHA AH+ A AHT G GH+ G GHC G GH+ G GH+ T TH+ T TH'
G G GH+ GH+
90 180 45 270 180 135 90 180 180 270 180 135 270 180
270 270 225 0 90 270 270 0 0 135 135 45 180 135
0.5 0.5 0.5 1.o 5.0 1.5 1 .o 5.0 0.5 1.5 5.0 0.5 1.o 5.0
135 315 180 270 90 180 0 135 45 180 225 135 135 315 315 45 135 135 135 45 135 225 45 180
225 135 315 90 225 45 270 90 0 90 315 90 315 225 0 0 315 0 0 0 0 135 270 135
0.5 0.5 1.o 5.0 1.o 1.5 0.5 5.0 0 1 .o 1.o 5.0 1.o 1.5 1 .o 5.0 0.5 1.5 1.o 5.0 0.5 1.5 1.5 5.0
-0.41 -0.30 -1.97 -1.94 44.07 -1.48 -5.35 43.28 -4.49 -5.17 43.46 -1.97 -3.91 46.71
-0.11
Heterogeneous Pairs
T T TH+ TH+ C C CH+ CH+ C C CHf CH+ T T TH+ TH+ C C CH' CH+
-
-1.61 -4.59 -2.46 44.08 -1.63 -4.52 -2.31 44.44 -1.65 -4.93 -2.93 45.86 -2.92 -4.27 -5.47 45.18 -3.87 -4.65 -4.46 43.54 -4.04 -5.20 -4.53 45.08
All interplanar distances set at 3.3 A ; starting geometrical arrangement as in Figure 1. Geometrical variations on variable geometry species defined according to clockwise rotation angle (RA) followed by clockwise translational angle (TRA) and translational distance (TRD). Monopole-monopole. Monopole-induced dipole (induced by species 2 in 1). e Monopole-induced dipole (induced by species 1 in 2). f Dispersion forces calculated from the species' own ionization potential. 0 Total interaction energy. a
45" increments over 360". For each rotational angle (RA) translations were performed in 45 O increments overo360"clockwise (TRA), and for each of thes: angles 0.5-A incremental variation up t o a total of 5-A translational distance (TRD) was allowed. Thus, the three geometrical variations RA, TRA, and T R D exactly define the position of the rotated group with respect to the stationary group. Table X quotes some of our results. Due to space limitations in most cases only the optimal interaction energies and the corresponding geometries are quoted. In most cases there were several regions of nearly optimal energies, however. Our main interest is to obtain relative values for the interaction energies as a function of base protonation. One needs to consider the pK,'s for the conjugate acids of the bases.5 These are 4.15 for N-1 protonation of adenine, 3.30 for N-7 protonation of guanine, 4.45 for (21) A list of optimal stacking energies and corresponding geometries
as well as the Fortran program performing the calculations are available from the authors upon request.
Jordan, Sostman
N-3 protonation of cytosine, and unknown (very low) for 0 - 4 protonation of t h ~ m i n e . ~While the values vary subtly in going from base t o nucleoside to nucleoside monophosphate, the relative orders remain the same. Thus, as the pH is lowered the relative ease of protonation follows the order cytosine > adenine > guanine > thymine. For completeness all possible pairing permutations were considered and are presented in Table X. We also calculated the stacking energies for doubly protonated pairs although as in our previous study' the results again indicate substantial destabilization of such pairs compared with the monoprotonated or neutral pairs. A natural separation of both stacking and hydrogenbonding interactions is in terms of self-stacking (homogeneous pairs) or mixed-stacking (heterogeneous pairs) interactions. Strictly speaking, such calculations apply only to the gaseous state. The effect of solvent is very difficult to predict. However, it has been experimentally established that stacking interactions are much stronger in an CNDOj2 and MIND0 Calculafions on Protonated DNA Bases
6550
aqueous medium22sand hydrogen bonding is observable both in nonaqueouszzband aqueouszzcsolutions of the bases. We have not considered the geometrical restrictions on the stacked bases present in polynucleotides but allowed complete freedom of the two stacked bases in searching out their optimum interaction energies. The values referred to in Table X represent such optimal values. Very significantly, our optimum interaction energies are in the range reported for stacking interactions by various authors on dinucleotides23 in aqueous solution and not very different from the theoretical values reported in ref 12c and 12d t o which they may be compared (subject to lack of knowledge of exact geometries in these references). Our own interest is in the effect of protonation on such interactions, and in this area there are relatively little experimental data reported. However, for sake of comparison with experimental results, the interactions of neutral species are also quoted, since to our knowledge the CND0/2 charges have not to date been used for this purpose. Homogeneous Pairs. Among neutral pairs the order of relative stability appears to be T-T > G-G > C-C > A-A, and all optimal geometries require rotation of the rotatable group t o some extent. While the absolute magnitudes for A-A, G-G, and C-C are similar, for T-T they appear t o be rather high. According t o ref 23d UpU (dinucleoside monophosphate) does stack. Some further experimental evidence indicates that methylation has significant effects on interactions. 5-Methyl poly C is more ordered than poly C.24 Poly T is helical; poly U is a random coil under the same condition^.^^ Poly G, poly C, poly U, and poly A are all capable of stacking under neutral pH conditionsz6 in agreement with the relatively large association energies here reported for all four homodimers. AHstacking values reportedz3 for the various neutral homodimers are in the range of 4-10 kcal/mol depending on the experimental determination employed. We could not find any experimental evidence for the self-stacking processes as a function of pH (especially near the pK). Protonation of one partner changes the order somewhat with decreasing order of stability, GH+-G > TH+-T > CH+-C > AH+-A. All half-protonated pairs have increased stabilities over their neutral counterparts, the enhanced stability being due to a combination of more favorable monopole-monopole and monopole-induced dipole terms in the half-protonated pairs. The increased induction energies of the four pairs upon protonation are relatively similar, whereas the per cent charge-charge interaction is much larger in purines (AH+-A > GH+-G) than in pyrimidines (CH +-C > TH+-T). (22) (a) S. Hanlon, Biochem. Biophys. Res. Commun., 23, 861 (1966); (b) Y.Kyogoku, R . C. Lord, and A. Rich, J. Amer. Chem. Soc., 89,496 (1967); (c) M. Raszka and N. 0. Kaplan, Proc. Nor. Acad. Sci. U. S., 69, 2025 (1972). (23) (a) J. Applequist and V. Damle, J . Amer. Chem. Soc., 88, 3895 (1966); (b) M. M. Warshaw and I. Tinoco, Jr., J . Mol. B i d , 20, 29 (1966); (c) J. Brahms, J. C. Maurizot, and A. M. Michelson, ibid., 25, 481 (1967); (d) R. C. Davis and I. Tinoco, Jr., Biopolymers, 6, 223 (1968). (24) W. Szer, M. Swierkowski, and D. Shugar, Acra Biochim. Pol., 10, 87 (1963). ( 2 5 ) W. Szer and D. Shugar, J. Mol. Biol., 17, 174 (1966). (26) A. M. Michelson, J. Massoulie, and W. Guschlbauer, Progr. Nucl. Acid Res. Mol. Biol., 6,83 (1967).
Journal of the American Chemical Society
Poly C and poly A both form double helices under acidic conditionsz6 (latter was discussed in ref 1); however, the ability to form the double helix is usually attributed to hydrogen bonding (vide infra). We are now proposing that the stacking interactions also become more favorable upon protonation of one partner. Double protonation of the pairs leads t o substantial electrostatic repulsions in all situations studied both in the hydrogen bonding and in the stacking modes. However, with the often invoked salt bridge between a base proton and a neighboring phosphate charge it is not too difficult t o rationalize the existence of such fully protonated forms on the basis of these calculations. T o overcome perhaps, e.g., 40 kcal/mol or more destabilization, the average distance between the phosphate - 1 charge an$ base 1 charge must be less than 331/40 or about 8 A. Depending on the charge concentration in the phosphate and base moieties, such salt bridge stabilization could be of paramount importance for these structures. In the absence of the double protonation the singly protonated pair could be further stabilized by the salt bridge. The problem of double protonation will not be further pursued since the experimental results are not very clear on this point either. Warshaw and T i n ~ c oindicated ~ ~ ~ that only a few dinucleoside monophosphates were stacked at pH 1 (GpC, CpG, UpG, GpU). In our view perhaps these represent half-protonated species. Heterogeneous Pairs. Stacking with Adenine. All neutral pairs containing adenine are more stable than A-A. On half-protonation all pairs become more stable than their neutral counterparts. Protonation of pyrimidine partners leads to greater stabilization than protonation of purine partners in a purine-pyrimidine stack. In an A-G stack AH+-G is more stable than A-GH+ Guanine-Containing Pairs. The neutral G-G or G-A interaction is less stable than the G-C or G-T interaction, though only the G-T interaction appears to be substantially different from the other three possibilities. Among half-protonated pairs purine-pyrimidine interactions are much more favorable upon pyrimidine protonation (especially for CH+-G pair us. C-GH+ pair). This latter pair may be particularly important at ordinary pH conditions considering the pK of cytosine protonation. It may be the one predominating at pH 123b~if monoprotonation (on C) perhaps suppresses the pK of G protonation in G-CH+, so that at this pH one is observing the half-protonated pair. Recently G p U was reported to stack only at low we also predict stabilization of the stack by G protonation. Thymine-Cytosine Pairs. This pair exhibits the smallest per cent stabilization of the half-protonated pair over the neutral pair of all the combinations studied. The stabilization of the stack due to protonation of either partner leads to remarkably similar values. Obviously, on thermodynamic grounds the CHf is much more available than the TH+. Hydrogen-Bonding Interactions. The results presented in Table XI represent values for the geometric arrangements drawn in structures I-XX. Most theoretically feasible arrangements have been accounted for with the assumption of the ribose (or deoxyribose)
+
(27) W. Guschlbauer, I. Fric, and A. Holy, Eur. J. Biochem., 31, 1 (1 972).
1 95:20 / October 3, 1973
6551 Table XI. Hydrogen-Bonding Interactions between DNA Bases as a Function of the State of Protonation Number“
Structureb
1-1
A-A
1-2
AH+-A
I1 111-1
A-A A-A
111-2 IV-1 IV-2 V VI VII-1 VII-2 VIII-1 VIII-2
AH+-A G-G GH+-G
IX x-1 x-2 XI XI1 XIII-1 XIII-2 XIV
xv-1
xv-2 xv-3 XVI-1 XVI-2 XVII-1 XVII-2 XVIII-1 XVIII-2 XIX
xx
1
H-bond distances,O 8, 2 3
-PPd
Interaction energies, kcal/mol--------. Pff(1P pa(2)f aao
Ebtalh
CH+-C T-T TH+-T T-Tmv T-TH+rev
2.81 2.90 2.87 2.95 2.93 2.88 2.96 2.90 2.86 2.84 2.92 2.90 2.98 2.87 2.87 2.87
2.81 2.90 2.89 2.96 2.93 2.87 2.97 2.92 2.86 2.79 2.92 2.84* 2.98 2.97 2.90 2.80
Homogeneous Pairs -0.93 -0.80 -1.73 -1.64 -1.41 -0.69 -0.63 -4.18 -7.39 -8.08 -3.84 2.85 -16.17 2.66 -9.27 3.12 -11.28
-0.16 -0.13 -0.14 -0.12 -0.13 -0.15 -0.13 -0.14 -0.63 -0.71 -0.33 -0.90 -0.28 -0.33 -0.34 -1.60
-0.16 -0.13 -2.43 -2.22 -0.13 -0.16 -0.13 -2.24 -0.63 -1.27 -0.33 -4.51 -0.28 -1.31 -0.38 -0.46
-3.36 -2.82 -4.14 -3.50 -2.43 -3.21 -2.72 -3.50 -1.87 -2.92 -2.81 -4.40 -1.38 -1.86 -1.68 -2.27
-4.60 -3.88 -8.45 -7.47 -4.11 -4.21 -3.60 -10.05 -10.53 -12.98 -7.31 -25.97’ 0.73 -12.77 0.72 -15.61
A-T A-T,,, A-TH+rey A-Crev A-CH+rev A-G,,” A-GH+rev A-GH+rev G-T GH+-T G-TH+ G-Trev GH+-T,e, G-C GH+-C T-C TH+-C CH+-T CH+-Trey
2.92 2.93 2.94 2.92 2.85* 2.92 2.89 2.86 2.86 2.83 2.88 2.83 2.87 2.92 2.86 2.84 2.85 2.87* 2.83*
2.85 2.89 2.89 2.90 2.86 2.84 2.84 2.94* 2.86 2.82 2.89 2.83 2.87 2.87 2.88 2.79 2.82 2.85 2.85
Heterogeneous Pairs 0.04 0.27 -6.57 -2.28 -7.11 -3.36 -4.85 -2.68 -0.15 -8.45 -10.98 -0.53 -8.88 2.86 -8.00 2.87 -11.19 2.35 2.85* -15.29 -11.45 -13.27
-0.40 -0.33 -4.27 -0.36 -4.94 -0.76 -1.91 -3.04 -0.36 -0.35 -1.85 -0.46 -0.40 -0.85 -0.77 -0.55 -0.76 -0.37 -0.49
-0.14 -0.14 -0.17 -0.13 -0.21 -0.17 -0.16 -0.12 -0.60 -1.35 -0.60 -0.62 -1.01 -0.78 -2.09 -0.41 -4.33 -2.22 -2.45
-2.47 -2.45 -3.81 -2.63 -4.45 -2.95 -3.34 -3.27 -2.16 -3.38 -2.33 -2.05 -2.46 -3.12 -3.94 -3.00 -4.27 -2.60 -2.76
-2.98 -2.66 -14.82 -5.41 -16.71 -7.23 -10.26 -9.10 -3.27 -13.54 -15.76 -3.64 -12.75 -12.75 -18.00 -1.61 - 24. 65i -16.64 -18.96
c-c
Numbering refers to the structures. * Protonation always on N-1 in AH+, N-7 in GH+, N-3 in CH+, and 0 - 4 in TH+; “normal” structures as drawn in Figure 1 ; reversed (rev) structures are the mirror image structures of those in Figure 1. Corresponding to the numbers in structures I-XX, starred hydrogen bond with attached proton. Monopole-monopole. e Monopole-induced dipole, induced in the first partner. J Monopole-induced dipole induced in the second partner. 0 Dispersion energy based on calculated ionization potential of each partner. Energy sum. a Structures with three hydrogen bonds.
being attached to N-9 of the purines and N-1 of the pyrimidines (see Figure 1 for numbering) and the site of protonation assumed at N-1 in A, N-7 in G, N-3 in C, and 0 - 4 in T. A geometric search was performed for a particular coplanar hydrogen-bonded pair which would allow for the most symmetrical and, in most cases, most linear hydrogen bond. Hydrogen-bonding distances for the A-T and G-C pairs are available and are approximately adhered t o throughout.28 The energy for any other separation along these essentially linear hydrogen bonds can be easily calculated for each contribution recalling that pp varies with d-I, p a with d-4, and aa with d-6 where the significance of the distances, d, associated with each term is discussed in ref 1. Homogeneous Pairs. Adenines. The configurations corresponding to structures 1-111 were calculated. Scheme 1-2 corresponds to the Hoogsteen scheme found in poly A with hydrogen bondsz9 at the N-6 and N-7 atoms. In this arrangement N-1 can be protonated (28) S. Amott, S. D. Dover, and A. J. Wonacott, Acta Crystallogr., Sect. B, 25,2192 (1969). (29) A. Rich, D. R. Davies, F. H. C. Crick, and J. D. Watson, J. Mol. Bioi., 3, 71 (1961).
Jordan, Sostman
and this protonation is shown t o lead to stabilization arising from both the p p and p a terms. At variance with the Pullman and Pullman theoretical results12 the three neutral pairs show remarkably similar stabilities. Protonation in arrangement 111 appears t o lead t o more stability than the protonation in the Hoogsteen scheme. (1-2). Only arrangements I and
/ CNDOIZ and M I N D 0 Calculations on Protonated DNA Bases
6552
I11 have precedents interestingly, lZa and these we predict t o be slightly more stable than 11. Some of these schemes supposedly help stabilize the double helical structures of monoprotonated and slightly more acidified polyriboadenylic acids. 30 Guanine. G-G hydrogen bonding via N-1 and 0 - 6 leads to an electrostatically ( p p ) much more stabilized system than any A-A pairs. Protonation of one partner on N-7 gives very small extra stabilization in this case (IV-1 and IV-2 and Table IV). This structure presumably occurs in poly G. Cytosine. While the C-C hydrogen bond is much stronger than the A-A hydrogen bond due to the pp term, it is somewhat weaker than the G-G hydrogen bond as suggested by ir experiments.32 Structure VI
a
is the scheme found in l-methylcyto~ine.~~ The halfprotonated pair (cannot be accomplished without movement of one base with respect t o the other) has capabilities of forming three hydrogen bonds (VI), one of which utilizes the proton acquired during protonation (on N-3). The CH+-C pair is shown to have an extraordinary stabilization (also suggested by Pullman l Z c and by several pieces of experimental evidence34). It is due in great part to the presence of three hydrogen bonds. However, it appears that protonation of cytosine is especially favorable for hydrogen-bond stabilization, since a comparison with the GH+-C structure (also with three hydrogen bonds) indicates that for essentially similar hydrogen-bond lengths the GH+-C system is very much less stabilized than the C-CH+ system due to both pp and p a type interactions. Thymine. There is a serious disagreement between our result and those of Pullman and Pullman'2c on the neutral pair. We predict no stabilization at all for this couple. Upon half-protonation both structures VI1 and VI11 become substantially stabilized, much less, however, than is CH+-C. Most recent evidence in H 2 0 indicates H-bonding self-association only for C-C and G-G pairszzcas suggested here. Heterogeneous Pairs. Adenine Pairs. Of greatest interest is A-T, structure IX, the Watson-Crick pairing scheme. To our great surprise this pair is not very (30) A. J. Adler, L. Grossman, and G. D. Fasman, Biochemistry, 8, 3846 (1969). (31) F. Pochon and A. M. Michelson, Proc. Nat. Acad. Sci. U. S., 53, 1425 (1965). (32) Y.Kyogoku, R.C. Lord, and A. Rich, Science, 154,518(1966). (33) F.S.Mathews and A. Rich, Nature (London), 201, 179 (1964). (34) (a) E.0.Akinrimisi, C. Sander, and P. 0.P. Ts'o, Biochemistry. 2,340 (1963); (b) T.M.Garestier and C. Helene, ibid., 9,2865 (1970).
Journal of the American Chemical Society
/
95:20
greatly stabilized. In fact, it is less stable than the A-A pair, the A-G pair, or the A-C pair but more stable than the T-T pair. It appears very likely that thymine is a relatively poor hydrogen-bonding partner (though it is an excellent stacking partner). In the WatsonCrick scheme (IX) A cannot be protonated at N-1 and
T cannot be protonated at 0-4. The scheme X-1,2 can accommodate T protonation leading to substantial stabilization again. This neutral scheme (X) is found in the X-ray structures of 9-ethyladenine with l-methyl5-iodouracil. 35 Cytosine and adenine can form a hydrogen-bonding scheme somewhat reminiscent of the Watson-Crick A-T pair (XI) but with the pyrimidine ring turned around. Upon protonation of the N-3 atom of cytosine this ring can slide up to form a very stable CH+-A complex (XII). Adenine and guanine can form a symmetrical hydrogen-bonding scheme (XIII). Two half-protonated
X \ [ 12
XIV
pairs may be found between A and GH+ (XIII-2 and XIV), their relative energies fairly similar t o each other. The neutral A-G pair appears to be the most stable one adenine is capable of forming. Guanine Pairs. Of greatest interest is the G-C pair suggested by Watson and Crick (scheme XVII). This is indicated to be the strongest neutral one of all those calculated as also indicated by experiments. 32,36 The pairing.allows N-7 protonation of G and this protona(35) T. D.Sakore, S. S. Tavale, and H. M. Sobell, J . Mol. Biol., 43, 361 (1969). (36) L. Katz and S. Penman, J . Mol. B i d , 15,220 (1966).
/ October 3, 1973
6553
tion leads t o further stabilization. The great stabilization of the G-C pair is undoubtedly due to the existence of three hydrogen bonds in scheme XVII. The calculations indicate that the C=O. . . N C hydrogen bond is somewhat stronger than are the C N . ‘ N C ones. Guanine is also suggested as a partner to thymine (schemes XV-XVII) with the G-T hydrogen bond being nearly the same energy as the A-T one. Protonation of either G (N-7) or T (0-4) under a variety of schemes indicates substantial further stabilization of the hydrogen bonds with the G-TH+ pairs preferred over the GH+-T pairs theoretically, while thermodynamically XIX
XVII-12
xx
CH
(Le., pK) it appears to be much easier t o protonate G
than T. Cytosine-Thymine. Possessing very similar stability of the neutral pair to T-T, protonation of C-T on either T (leads to three hydrogen bonds and exceptional stability) or C (leads to two hydrogen bonds only but very great stability, e.g., schemes XIX and XX) again is very favorable thermodynamically. One would, of course, expect the C to be much more easily protonated than T. Realistically, one needs to consider the ease of protonation of each partner (Le., pKa’s of the conjugate acid) to decide if any of the proposed schemes are feasible or not. Intrinsically, the calculations apply to the gaseous state only. Undoubtedly the solvent would have substantial effects on the pKa’s in the di-, tri-, and polynucleotides. T o our knowledge no exact values of first and second protonation p K s are known for any of the cases of interest, undoubtedly due t o the experimental difficulties encountered in determining sites and equilibrium constants of protonation in these systems. For example, it is certainly not unreasonable to expect that the pK for second protonation will be profoundly influenced by the first base protonation in the pair. The more recent aqueous work indicates hydrogen bonding in GMP-UMP, AMP-CMP, and CMPUMP pairs along with weaker bonds in GMP-CMP andAMP-UMP.22c Critical Evaluation of Results As all other calculations before ours, the present work also suffers from some obvious theoretical approximations. It is worth emphasizing that we have chosen a method which is uniformly applicable to both neutral and protonated interacting species. While results on neutral pair interactions abound, l 2 ours is the first attempt to compare neutral pair interactions with half- and fully
protonated pair ones. Many of our results on neutral pairs qualitatively follow those of Pullman and Pullman,lZebut one still should not forget that even different physical methods predict quite different interaction enthalpies for the neutral pairs. 37 The present approach includes only the monopolemonopole, monopole-induced dipole, and induced dipole-induced dipole terms in the intermolecular potential. The results are reported for fixed intermolecular separations, such separations being taken from available X-ray data. We d o not expect that the calculations, as a function of intermolecular separation, would lead to a minimum energy geometry, since no repulsion (for example, of a Lennard-Jones or other nonbonded type) term is included. Our aim is, as a first approximation, to compare the interaction energies for very similar stacking and hydrogen-bonding distances varying only the possible arrangement of interacting species. Our interaction energies for neutral pairs are somewhat lower than those quoted from other theory, probably because of our underestimate of net atomic charges. 37a Our calculations give interaction energies closer to experimental values. Disagreement between our results and those of Pullman and PullmanlZeare due to several factors (aside from our lack of knowledge of the precise geometric input employed by the other group). Our monopole-monopole term is calculated with CND0/2 net atomic charges. The reasonable dipole moments predicted by C N D 0 / 2 are, however, due to the inclusion of the hybrid moment contribution3r4 (monoatomic overlap charges). Without this second term the dipole moment is too small and the electron density map is not invariant to rotation of coordinate axes. Previous studies12e employed u 7r net atomic charges which directly yielded reasonable dipole moments in a point charge approximation. Thus our net atomic charges (hence pp and p a terms) are bound to be much smaller than those quoted by Pullman and Pullman.12e The variation in pp terms is most evident in our much smaller hydrogen-bonding interaction energies. Using isotropic bond polarizabilities and the ionization potentials previously quoted, we obtain larger dispersion terms (aa) than those referenced l Z e which employed smaller ionization potentials. We feel that, for the present, the C N D 0 / 2 net atomic charges represent a consistent approach to the monopole-monopole and monopole-induced dipole terms when comparing neutral to protonated substrate interactions. While the u A approach, mimicking correct dipole moments in neutral species, is useful, its application to charged species is of doubtful value since in the latter one has no obvious experimental quantity t o mimic. We are not at all certain that an iterated extended Hiickel charge density calculation is any more meaningful than the-one here employed, assuming such gives reasonable dipole moments for neutral species. Improved intermolecular potential calculations with ab
+
+
(37) (a) N. I
